| """ |
| Performance Take-Home: Optimize build_kernel for a VLIW SIMD processor. |
| |
| The goal is to minimize CPU cycles for a parallel tree traversal algorithm. |
| The program runs on a simulated VLIW SIMD processor with these slot limits per cycle: |
| - ALU: 12 scalar operations |
| - VALU: 6 vector operations (8-element SIMD vectors) |
| - Load: 2 memory reads |
| - Store: 2 memory writes |
| - Flow: 1 control flow instruction |
| |
| Key optimization strategies: |
| - VLIW parallelism: pack independent ops into single cycles |
| - SIMD vectorization: process 8 batch elements per vector instruction |
| - Loop unrolling to reduce overhead |
| - Instruction scheduling to maximize ILP |
| - Use multiply_add for certain hash stages |
| - Minimize load/store by reusing scratch values |
| |
| The algorithm: |
| For each round (16 rounds): |
| For each batch element (256 elements): |
| 1. Load idx and val from memory |
| 2. Load node_val = forest[idx] |
| 3. val = hash(val ^ node_val) -- 6-stage hash |
| 4. idx = 2*idx + (1 if val%2==0 else 2) |
| 5. if idx >= n_nodes: idx = 0 |
| 6. Store idx and val back |
| |
| HASH_STAGES (each stage: op1, val1, op2, op3, val3): |
| ("+", 0x7ED55D16, "+", "<<", 12) |
| ("^", 0xC761C23C, "^", ">>", 19) |
| ("+", 0x165667B1, "+", "<<", 5) |
| ("+", 0xD3A2646C, "^", "<<", 9) |
| ("+", 0xFD7046C5, "+", "<<", 3) |
| ("^", 0xB55A4F09, "^", ">>", 16) |
| |
| Each hash stage computes: |
| tmp1 = op1(val, val1) |
| tmp2 = op3(val, val3) |
| val = op2(tmp1, tmp2) |
| |
| Available instructions: |
| ALU: (op, dst, src1, src2) where op in +, -, *, /, %, ^, &, |, <<, >>, ==, !=, <, >, <=, >= |
| Also: ("multiply_add", dst, a, b, c) => dst = a*b + c |
| VALU: same ops but on 8-element vectors, e.g. ("+", vdst, vsrc1, vsrc2) |
| Load: ("load", dst_scratch, addr_scratch) - load mem[scratch[addr]] into scratch[dst] |
| ("const", dst_scratch, value) - store constant into scratch[dst] |
| ("vload", vdst, addr_scratch) - load 8 contiguous words from mem[scratch[addr]] |
| ("vbroadcast", vdst, scalar_scratch) - broadcast scalar to all 8 vector lanes |
| Store: ("store", addr_scratch, src_scratch) - store scratch[src] to mem[scratch[addr]] |
| ("vstore", addr_scratch, vsrc) - store 8 words to mem[scratch[addr]] |
| Flow: ("select", dst, cond, true_val, false_val) - conditional select |
| ("vselect", vdst, vcond, vtrue, vfalse) - vector conditional select |
| ("jump", target_pc) - unconditional jump |
| ("cond_jump", cond_scratch, target_pc) - conditional jump |
| ("pause",) - pause execution (ignored in submission) |
| ("halt",) - stop execution |
| Debug: ("comment", text), ("compare", addr, key) - ignored in submission |
| |
| Scratch space: 1536 words total. Each alloc_scratch(name, length) reserves contiguous words. |
| Vector scratch: alloc_scratch(name, 8) reserves 8 contiguous words for a vector register. |
| |
| IMPORTANT VLIW NOTES: |
| - All effects in a cycle are applied atomically at end of cycle |
| - You can read a value and write to it in the same cycle |
| - Multiple engines execute in parallel within one instruction bundle |
| - An instruction bundle is a dict mapping engine names to lists of slots: |
| e.g. {"alu": [(...), (...)], "load": [(...), (...)], "valu": [(...), (...)]} |
| |
| Baseline (naive scalar): 147,734 cycles |
| Best known: 1,363 cycles (108x speedup) |
| """ |
|
|
| import sys |
| import os |
|
|
| sys.path.insert(0, os.path.join(os.path.dirname(__file__), "problem_src")) |
|
|
| from problem import ( |
| Engine, |
| DebugInfo, |
| SLOT_LIMITS, |
| VLEN, |
| N_CORES, |
| SCRATCH_SIZE, |
| Machine, |
| Tree, |
| Input, |
| HASH_STAGES, |
| reference_kernel, |
| build_mem_image, |
| reference_kernel2, |
| ) |
|
|
| from collections import defaultdict |
|
|
|
|
| |
| class KernelBuilder: |
| def __init__(self): |
| self.instrs = [] |
| self.scratch = {} |
| self.scratch_debug = {} |
| self.scratch_ptr = 0 |
| self.const_map = {} |
|
|
| def debug_info(self): |
| return DebugInfo(scratch_map=self.scratch_debug) |
|
|
| def build(self, slots: list[tuple[Engine, tuple]], vliw: bool = False): |
| |
| instrs = [] |
| for engine, slot in slots: |
| instrs.append({engine: [slot]}) |
| return instrs |
|
|
| def add(self, engine, slot): |
| self.instrs.append({engine: [slot]}) |
|
|
| def alloc_scratch(self, name=None, length=1): |
| addr = self.scratch_ptr |
| if name is not None: |
| self.scratch[name] = addr |
| self.scratch_debug[addr] = (name, length) |
| self.scratch_ptr += length |
| assert self.scratch_ptr <= SCRATCH_SIZE, "Out of scratch space" |
| return addr |
|
|
| def scratch_const(self, val, name=None): |
| if val not in self.const_map: |
| addr = self.alloc_scratch(name) |
| self.add("load", ("const", addr, val)) |
| self.const_map[val] = addr |
| return self.const_map[val] |
|
|
| def build_hash(self, val_hash_addr, tmp1, tmp2, round, i): |
| slots = [] |
|
|
| for hi, (op1, val1, op2, op3, val3) in enumerate(HASH_STAGES): |
| slots.append(("alu", (op1, tmp1, val_hash_addr, self.scratch_const(val1)))) |
| slots.append(("alu", (op3, tmp2, val_hash_addr, self.scratch_const(val3)))) |
| slots.append(("alu", (op2, val_hash_addr, tmp1, tmp2))) |
| slots.append(("debug", ("compare", val_hash_addr, (round, i, "hash_stage", hi)))) |
|
|
| return slots |
|
|
| def build_kernel( |
| self, forest_height: int, n_nodes: int, batch_size: int, rounds: int |
| ): |
| """ |
| Like reference_kernel2 but building actual instructions. |
| Scalar implementation using only scalar ALU and load/store. |
| """ |
| tmp1 = self.alloc_scratch("tmp1") |
| tmp2 = self.alloc_scratch("tmp2") |
| tmp3 = self.alloc_scratch("tmp3") |
| |
| init_vars = [ |
| "rounds", |
| "n_nodes", |
| "batch_size", |
| "forest_height", |
| "forest_values_p", |
| "inp_indices_p", |
| "inp_values_p", |
| ] |
| for v in init_vars: |
| self.alloc_scratch(v, 1) |
| for i, v in enumerate(init_vars): |
| self.add("load", ("const", tmp1, i)) |
| self.add("load", ("load", self.scratch[v], tmp1)) |
|
|
| zero_const = self.scratch_const(0) |
| one_const = self.scratch_const(1) |
| two_const = self.scratch_const(2) |
|
|
| self.add("flow", ("pause",)) |
| self.add("debug", ("comment", "Starting loop")) |
|
|
| body = [] |
|
|
| |
| tmp_idx = self.alloc_scratch("tmp_idx") |
| tmp_val = self.alloc_scratch("tmp_val") |
| tmp_node_val = self.alloc_scratch("tmp_node_val") |
| tmp_addr = self.alloc_scratch("tmp_addr") |
|
|
| for round in range(rounds): |
| for i in range(batch_size): |
| i_const = self.scratch_const(i) |
| |
| body.append(("alu", ("+", tmp_addr, self.scratch["inp_indices_p"], i_const))) |
| body.append(("load", ("load", tmp_idx, tmp_addr))) |
| body.append(("debug", ("compare", tmp_idx, (round, i, "idx")))) |
| |
| body.append(("alu", ("+", tmp_addr, self.scratch["inp_values_p"], i_const))) |
| body.append(("load", ("load", tmp_val, tmp_addr))) |
| body.append(("debug", ("compare", tmp_val, (round, i, "val")))) |
| |
| body.append(("alu", ("+", tmp_addr, self.scratch["forest_values_p"], tmp_idx))) |
| body.append(("load", ("load", tmp_node_val, tmp_addr))) |
| body.append(("debug", ("compare", tmp_node_val, (round, i, "node_val")))) |
| |
| body.append(("alu", ("^", tmp_val, tmp_val, tmp_node_val))) |
| body.extend(self.build_hash(tmp_val, tmp1, tmp2, round, i)) |
| body.append(("debug", ("compare", tmp_val, (round, i, "hashed_val")))) |
| |
| body.append(("alu", ("%", tmp1, tmp_val, two_const))) |
| body.append(("alu", ("==", tmp1, tmp1, zero_const))) |
| body.append(("flow", ("select", tmp3, tmp1, one_const, two_const))) |
| body.append(("alu", ("*", tmp_idx, tmp_idx, two_const))) |
| body.append(("alu", ("+", tmp_idx, tmp_idx, tmp3))) |
| body.append(("debug", ("compare", tmp_idx, (round, i, "next_idx")))) |
| |
| body.append(("alu", ("<", tmp1, tmp_idx, self.scratch["n_nodes"]))) |
| body.append(("flow", ("select", tmp_idx, tmp1, tmp_idx, zero_const))) |
| body.append(("debug", ("compare", tmp_idx, (round, i, "wrapped_idx")))) |
| |
| body.append(("alu", ("+", tmp_addr, self.scratch["inp_indices_p"], i_const))) |
| body.append(("store", ("store", tmp_addr, tmp_idx))) |
| |
| body.append(("alu", ("+", tmp_addr, self.scratch["inp_values_p"], i_const))) |
| body.append(("store", ("store", tmp_addr, tmp_val))) |
|
|
| body_instrs = self.build(body) |
| self.instrs.extend(body_instrs) |
| |
| self.instrs.append({"flow": [("pause",)]}) |
| |
|
|