Single Tile Matvec
Contents
Single Tile Matvec¶
This program performs single tile matrix-vector products y = A*x,
where A has dimension N x N, and the data type is fp32.
This program produces memory bandwidth information and FLOPS.
To compile and run for N=10 to N=100 on an actual CS-2, use:
./sweep.py --dims 750,994 --cmaddr <CS IP ADDR>
Dims here refers to the dimensions of the program rectangle. The program above will perform 750*994 matvecs, with one matvec occurring on each PE, for each value of N.
There is also an iters flag, which allows you to average
cycle counts over multiple runs. Here is an example for a
10 x 10 program rectangle run in the simulator:
./sweep.py --dims 10,10 --iters 10.
You can also compile and run separately, and also run in a verificaiton mode that verifies the result on each PE.
To compile:
cslc layout_matvec.csl --fabric-dims=17,12 --fabric-offsets=4,1 \
--params=width:10,height:10,tile_size:25,iters:1 -o out --memcpy --channels=1
where fabric-dims is the dimension of the simfabric, width, height
are the dimensions of the program rectangle, tile_size is N,
and iters is the number of iterations over which we average.
Note that the width must be no bigger than 7 less than the x-dimension of the fabric, and the height must be no bigger than 2 less than the y-dimension of the fabric.
Additionally, if you are running on a real CS-2, fabric-dims must
be 750,994.
To run:
cs_python run.py --name out --verify
where the --verify flag verifies the result on each PE.
Note that this flag is incompatible with any number of iterations greater than 1.
Again, pass --cmaddr to run on a real CS-2.
If you’re just running on simfabric, there’s no need to use a width or height
greater than one. The cycle counts will be the same across all simulated PEs.
The program will report a “relative” and “absolute” memory bandwidth. Relative refers to the bandwidth obtained if we calculate based on the number of memory accesses that would occur to implement a matrix-vector product on a more traditional architecture, where caching allows us to write the y vector for example, only once to memory. “Absolute” refers to the actual number of memory accesses required to run this program on the WSE. See comments in the code for more details.
layout_matvec.csl¶
param width: u16;
param height: u16;
param tile_size: u16;
param iters: u16;
const memcpy = @import_module("<memcpy/get_params>", .{
.width = width,
.height = height,
});
layout {
@set_rectangle(width, height);
for (@range(u16, width)) |px| {
const memcpy_params = memcpy.get_params(px);
for (@range(u16, height)) |py| {
@set_tile_code(px, py, "pe_matvec.csl", .{ .memcpy_params = memcpy_params,
.nb = tile_size, .iters = iters});
}
}
// export symbol names
@export_name("A", [*]f32, true);
@export_name("x", [*]f32, true);
@export_name("y", [*]f32, true);
@export_name("maxmin_time", [*]f32, true);
@export_name("compute", fn()void);
}
pe_matvec.csl¶
param memcpy_params: comptime_struct;
param nb: u16; // array tile size, corresponds to matrix dimension
param iters: u16; // num iterations to run matvec
const EXIT: local_task_id = @get_local_task_id(9); // entrypoint to leave RPC
// alignment calculation
const pad_align: u16 = 16;
const elem_size: u16 = 4;
const align_ratio: u16 = pad_align / elem_size;
const padded_nb: u16 = if ((nb / align_ratio) * align_ratio == nb) nb
else (nb / align_ratio + 1) * align_ratio;
const sys_mod = @import_module("<memcpy/memcpy>", memcpy_params);
const timestamp = @import_module("<time>");
var tsc_end_buf = @zeros([timestamp.tsc_size_words]u16);
var tsc_start_buf = @zeros([timestamp.tsc_size_words]u16);
var timer_buf = @zeros([3]f32);
var ptr_timer_buf: [*]f32 = &timer_buf;
var A_array: [nb*padded_nb+1]f32 align(16) = @zeros([nb*padded_nb+1]f32);
var x_array: [nb]f32 align(16) = @zeros([nb]f32);
var y_array: [padded_nb]f32 align(16) = @zeros([padded_nb]f32);
var ptr_A: [*]f32 = &A_array;
var ptr_x: [*]f32 = &x_array;
var ptr_y: [*]f32 = &y_array;
var A_dsd = @get_dsd(mem1d_dsd, .{ .tensor_access = |i|{padded_nb} -> A_array[i+1] });
var x_dsd = @get_dsd(mem1d_dsd, .{ .tensor_access = |i|{nb} -> x_array[i] });
var y_dsd = @get_dsd(mem1d_dsd, .{ .tensor_access = |i|{padded_nb} -> y_array[i] });
const y_dest_dsr = @get_dsr(dsr_dest, 0);
const y_src0_dsr = @get_dsr(dsr_src0, 0);
const A_src1_dsr = @get_dsr(dsr_src1, 0);
fn gemv_static_step_A(curX: f32) void {
@fmacs(y_dest_dsr, y_src0_dsr, A_src1_dsr, curX);
}
fn gemv_map() void {
// COMPUTE //
/////////////
// A * X = Y
////////////
var local_A_dsd: mem1d_dsd = A_dsd;
var local_y_dsd: mem1d_dsd = y_dsd;
@load_to_dsr(y_dest_dsr, local_y_dsd, .{ .save_address = false });
@load_to_dsr(y_src0_dsr, local_y_dsd, .{ .save_address = false });
@load_to_dsr(A_src1_dsr, local_A_dsd, .{ .save_address = true });
@map(gemv_static_step_A, x_dsd);
}
fn compute() void {
timestamp.enable_tsc();
timestamp.get_timestamp(&tsc_start_buf);
for (@range(u16, iters)) |iter| {
gemv_map();
}
timestamp.get_timestamp(&tsc_end_buf);
timestamp.disable_tsc();
var lo_: u16 = 0;
var hi_: u16 = 0;
var word: u32 = 0;
lo_ = tsc_start_buf[0];
hi_ = tsc_start_buf[1];
timer_buf[0] = @bitcast(f32, (@as(u32,hi_) << @as(u16,16)) | @as(u32, lo_) );
lo_ = tsc_start_buf[2];
hi_ = tsc_end_buf[0];
timer_buf[1] = @bitcast(f32, (@as(u32,hi_) << @as(u16,16)) | @as(u32, lo_) );
lo_ = tsc_end_buf[1];
hi_ = tsc_end_buf[2];
timer_buf[2] = @bitcast(f32, (@as(u32,hi_) << @as(u16,16)) | @as(u32, lo_) );
@activate(EXIT);
}
task f_exit() void {
// the user must unblock cmd color for every PE
sys_mod.unblock_cmd_stream();
}
comptime {
@bind_local_task(f_exit, EXIT);
@export_symbol(ptr_A, "A");
@export_symbol(ptr_x, "x");
@export_symbol(ptr_y, "y");
@export_symbol(ptr_timer_buf, "maxmin_time");
@export_symbol(compute);
}
run.py¶
#!/usr/bin/env cs_python
# pylint: disable=line-too-long,too-many-function-args
import struct
import time
import argparse
import math
import csv
import json
import numpy as np
from cerebras.sdk.runtime.sdkruntimepybind import SdkRuntime # pylint: disable=no-name-in-module
from cerebras.sdk.runtime.sdkruntimepybind import MemcpyDataType, MemcpyOrder # pylint: disable=no-name-in-module
def parse_args():
""" parse the command line """
parser = argparse.ArgumentParser(description="single tile matvec run parameters")
parser.add_argument("--name", required=False, default="out",
help="prefix of ELF files")
parser.add_argument("--cmaddr", required=False, default="",
help="IP:port for CS system")
parser.add_argument("--verify", action="store_true",
help="Verify Y computation")
args = parser.parse_args()
return args
def float_to_hex(f):
return hex(struct.unpack('<I', struct.pack('<f', f))[0])
def make_u48(words):
return words[0] + (words[1] << 16) + (words[2] << 32)
def sub_ts(words):
return make_u48(words[3:]) - make_u48(words[0:3])
def main():
"""Main method to run the example code."""
args = parse_args()
name = args.name
cmaddr = args.cmaddr
verify = args.verify
# Parse the compile metadata
with open(f"{name}/out.json", encoding="utf-8") as json_file:
compile_data = json.load(json_file)
nb = int(compile_data["params"]["tile_size"])
width = int(compile_data["params"]["width"])
height = int(compile_data["params"]["height"])
iters = int(compile_data["params"]["iters"])
# Calculate alignment and padding to avoid bank conflicts
align = 16
multiple = int(align/4)
padded_nb = math.ceil(nb/multiple)*multiple
#############
# Run
#############
start = time.time()
# Instantiate runner
runner = SdkRuntime(name, cmaddr=cmaddr)
# Device symbols for memcpy
A_symbol = runner.get_id("A")
x_symbol = runner.get_id("x")
y_symbol = runner.get_id("y")
symbol_maxmin_time = runner.get_id("maxmin_time")
# Load and begin run
runner.load()
runner.run()
# Construct A data and copy random A matrix PE (0,0) for verification
A_mat = np.random.rand(nb, nb)
A_data = np.zeros(width*height*(nb*padded_nb+1), dtype=np.float32)
for w in range(width):
for h in range(height):
for i in range(nb):
for j in range(nb):
A_data[(h*width + w)*(nb*padded_nb+1) + j*padded_nb + i + 1] = A_mat[i, j]
print()
print("Beginning run.")
print("Copy A matrices to device...")
runner.memcpy_h2d(A_symbol, A_data, 0, 0, width, height, nb*padded_nb+1,
streaming=False, data_type=MemcpyDataType.MEMCPY_32BIT, order=MemcpyOrder.ROW_MAJOR, nonblock=False)
# Construct x data and copy random x vector to PE (0,0) for verification
x_vec = np.random.rand(nb)
x_data = np.zeros(width*height*nb, dtype=np.float32)
for w in range(width):
for h in range(height):
x_data[(h*width + w)*nb:(h*width + w)*nb+nb] = x_vec
print("Copy x vectors to device...")
runner.memcpy_h2d(x_symbol, x_data, 0, 0, width, height, nb,
streaming=False, data_type=MemcpyDataType.MEMCPY_32BIT, order=MemcpyOrder.ROW_MAJOR, nonblock=False)
# Launch the compute kernel
print("Launch kernel...")
runner.call("compute", [], nonblock=False)
# Copy back timestamps from device
data = np.zeros((width*height*3, 1), dtype=np.uint32)
runner.memcpy_d2h(data, symbol_maxmin_time, 0, 0, width, height, 3,
streaming=False, data_type=MemcpyDataType.MEMCPY_32BIT, order=MemcpyOrder.ROW_MAJOR, nonblock=False)
maxmin_time_hwl = data.view(np.float32).reshape((height, width, 3))
print("Copied back timestamps.")
# Copy back data array from device
if verify:
data = np.zeros((width*height*padded_nb, 1), dtype=np.uint32)
runner.memcpy_d2h(data, y_symbol, 0, 0, width, height, padded_nb,
streaming=False, data_type=MemcpyDataType.MEMCPY_32BIT, order=MemcpyOrder.ROW_MAJOR, nonblock=False)
y_device_array = data.view(np.float32).reshape((height, width, padded_nb))
print("Copied back Y array.")
print("Done.")
# End walltime timer
runner.stop()
end = time.time()
walltime = end-start
###########
# Verify
###########
if verify:
print("Test y result is as expected on each PE...")
expected = A_mat @ x_vec
for w in range(width):
for h in range(height):
np.testing.assert_allclose(y_device_array[h, w, :nb], expected, atol=0.0001, rtol=0)
print("SUCCESS!")
#################################
# Calculate mem accesses and FLOP
#################################
# STANDARD read/writes
# Read full x, read each column of V stack, write full y = nb + nb*nb + nb
# = nb*nb + 2*nb
#
# 4 bytes per elem. Mem = 4 * (nb*nb + 2*nb)
# = 4*nb*nb + 8*nb
# ACTUAL read/writes
# Read full x; read each col of V stack; read, write full y nb times
# = nb + nb*nb + 2*nb*nb
# = 3*nb*nb + nb
#
# 4 bytes per elem. Mem = 4 * (3*nb*nb + nb)
# = 12*nb*nb + 4*nb
# Floating point operations
# Compute A_ij * x_j for each i, j = nb * nb
# For each row of A, reduction uses nb - 1 adds = nb * (nb-1)
# = nb * nb + nb * (nb-1)
# = 2*nb*nb - nb
total_relative_accesses = width * height * (4*nb*nb + 8*nb)
total_absolute_accesses = width * height * (12*nb*nb + 4*nb)
total_flop = width * height * (2*nb*nb - nb)
#######################
# Calculate cycle count
#######################
tsc_tensor_d2h = np.zeros(6).astype(np.uint16)
min_cycles = math.inf
max_cycles = 0
for w in range(width):
for h in range(height):
hex_t0 = int(float_to_hex(maxmin_time_hwl[(h, w, 0)]), base=16)
hex_t1 = int(float_to_hex(maxmin_time_hwl[(h, w, 1)]), base=16)
hex_t2 = int(float_to_hex(maxmin_time_hwl[(h, w, 2)]), base=16)
tsc_tensor_d2h[0] = hex_t0 & 0x0000ffff
tsc_tensor_d2h[1] = (hex_t0 >> 16) & 0x0000ffff
tsc_tensor_d2h[2] = hex_t1 & 0x0000ffff
tsc_tensor_d2h[3] = (hex_t1 >> 16) & 0x0000ffff
tsc_tensor_d2h[4] = hex_t2 & 0x0000ffff
tsc_tensor_d2h[5] = (hex_t2 >> 16) & 0x0000ffff
cycles = sub_ts(tsc_tensor_d2h)
if cycles < min_cycles:
min_cycles = cycles
min_w = w
min_h = h
if cycles > max_cycles:
max_cycles = cycles
max_w = w
max_h = h
#####################
# Calculate bandwidth
#####################
# Calculate in bytes/sec and FLOP/sec for program rectangle
secs = max_cycles / 850000000.
relative_bw = total_relative_accesses / secs * iters
absolute_bw = total_absolute_accesses / secs * iters
flops_sec = total_flop / secs
# Convert to Petabytes/sec and PetaFLOPS
relative_bw /= 1.E15
absolute_bw /= 1.E15
flops_sec /= 1.E15
# Scale to program rectangle
scale_factor = (994.*750.) / (width*height)
scale_relative_bw = relative_bw * scale_factor
scale_absolute_bw = absolute_bw * scale_factor
scale_flops_sec = flops_sec * scale_factor
#################
# Generate output
#################
print()
print(f"Real walltime: {walltime}s")
print()
print("Cycle Counts:")
print("Min cycles (", min_w, ", ", min_h, "): ", min_cycles)
print("Max cycles (", max_w, ", ", max_h, "): ", max_cycles)
print()
print("Accesses and FLOP Information:")
print("Relative accesses (bytes): ", total_relative_accesses)
print("Absolute accesses (bytes): ", total_absolute_accesses)
print("FP operations: ", total_flop)
print()
print("Bandwidth and FLOPS Information:")
print("Relative BW (PB/s): ", relative_bw)
print("Absolute BW (PB/s): ", absolute_bw)
print("PetaFLOPS: ", flops_sec)
print()
print("Scaled (", width, ",", height, ") to (750,994)...")
print("Scaled relative BW (PB/s): ", scale_relative_bw)
print("Scaled absolute BW (PB/s): ", scale_absolute_bw)
print("Scaled PetaFLOPS: ", scale_flops_sec)
# Write a CSV
csv_name = name + ".csv"
with open(csv_name, mode='a') as csv_file:
csv_writer = csv.writer(csv_file)
csv_writer.writerow([cmaddr, width, height, iters, nb, padded_nb, min_cycles, max_cycles,
total_relative_accesses, total_absolute_accesses, relative_bw, absolute_bw,
scale_relative_bw, scale_absolute_bw, total_flop, flops_sec, scale_flops_sec, walltime])
if __name__ == "__main__":
main()
commands.sh¶
#!/usr/bin/env bash
set -e
cslc ./layout_matvec.csl --arch wse2 --fabric-dims=9,4 \
--fabric-offsets=4,1 \
--params=width:2,height:2,tile_size:25,iters:1 \
-o out --memcpy --channels=1
cs_python ./run.py --name out --verify
sweep.py¶
#!/usr/bin/env python
import subprocess
import argparse
def parse_args():
""" parse the command line """
parser = argparse.ArgumentParser(description="Sweep single tile matvec size parameter")
parser.add_argument("--name", required=False, default="out",
help="Prefix of ELF files")
parser.add_argument("--cmaddr", required=False, default="",
help="IP:port for CS system")
parser.add_argument("--dims",
help="Fabric and program dimension, i.e. <W>,<H>")
parser.add_argument("--iters", required=False, type=int, default=1,
help="Number of iterations for each matvec")
args = parser.parse_args()
return args
def cslc_compile(
width: int,
height: int,
tile_size: int,
iters: int,
name: str
):
"""Generate ELFs for the layout"""
args = []
args.append("cslc") # command
args.append(f"layout_matvec.csl") # file
args.append(f"--fabric-dims={width+7},{height+2}") # options
args.append("--fabric-offsets=4,1")
args.append(f"--params=width:{width},height:{height},tile_size:{tile_size},iters:{iters}")
args.append(f"-o={name}")
args.append("--arch=wse2")
args.append("--memcpy")
args.append("--channels=1")
print(f"subprocess.check_call(args = {args}")
subprocess.check_call(args)
def cs_run(
name: str,
cmaddr: str
):
"""Run with cs_python"""
args = []
args.append("cs_python")
args.append("run.py")
args.append(f"--name={name}")
args.append(f"--cmaddr={cmaddr}")
subprocess.check_call(args)
def compile_and_run(
width: int,
height: int,
tile_size: int,
iters: int,
name: str,
cmaddr: str
):
"""Compile and run program."""
cslc_compile(
width,
height,
tile_size,
iters,
name)
cs_run(name, cmaddr)
def main():
"""Main method to run the example code."""
args = parse_args()
w, h = args.dims.split(",")
width = int(w)
height = int(h)
name = args.name # compilation output
cmaddr = args.cmaddr
iters = args.iters
for tile_size in range(10,101,10):
compile_and_run(
width,
height,
tile_size,
iters,
name,
cmaddr)
if __name__ == "__main__":
main()