#! /usr/bin/python import random, math, os, re from twisted.python import usage class Args(usage.Options): optParameters = [ ["mode", "m", "alpha", "validation scheme"], ["arity", "k", 2, "k (airty) for hash tree"], ] def opt_arity(self, option): self['arity'] = int(option) def parseArgs(self, *args): if len(args) > 0: self['mode'] = args[0] def charttest(): import gdchart sizes = [random.randrange(10, 20) for i in range(10)] x = gdchart.Line() x.width = 250 x.height = 250 x.xtitle = "sample" x.ytitle = "size" x.title = "Example Graph" #x.ext_color = [ "white", "yellow", "red", "blue", "green"] x.setData(sizes) #x.setLabels(["Mon", "Tue", "Wed", "Thu", "Fri"]) x.draw("simple.png") KiB=1024 MiB=1024*KiB GiB=1024*MiB TiB=1024*GiB PiB=1024*TiB class Sizes: def __init__(self, mode, file_size, arity=2): MAX_SEGSIZE = 2*MiB self.mode = mode self.file_size = file_size self.seg_size = seg_size = 1.0 * min(MAX_SEGSIZE, file_size) self.num_segs = num_segs = math.ceil(file_size / seg_size) self.num_subblocks = num_subblocks = num_segs self.num_blocks = num_blocks = 100 self.blocks_needed = blocks_needed = 25 self.subblock_size = subblock_size = seg_size / blocks_needed self.block_size = block_size = subblock_size * num_subblocks # none of this includes the block-level hash chain yet, since that is # only a function of the number of blocks. All overhead numbers # assume that the block-level hash chain has already been sent, # including the root of the subblock-level hash tree. if mode == "alpha": # no hash tree at all self.subblock_arity = 0 self.subblock_tree_depth = 0 self.subblock_overhead = 0 self.bytes_until_some_data = 20 + block_size self.block_storage_overhead = 0 self.block_transmission_overhead = 0 elif mode == "beta": # k=num_subblocks, d=1 # each subblock has a 20-byte hash self.subblock_arity = num_subblocks self.subblock_tree_depth = 1 self.subblock_overhead = 20 # the block has a list of hashes, one for each subblock self.block_storage_overhead = (self.subblock_overhead * num_subblocks) # we can get away with not sending the hash of the block that # we're sending in full, once self.block_transmission_overhead = self.block_storage_overhead - 20 # we must get the whole list (so it can be validated) before # any data can be validated self.bytes_until_some_data = (self.block_transmission_overhead + subblock_size) elif mode == "gamma": self.subblock_arity = k = arity d = math.ceil(math.log(num_subblocks, k)) self.subblock_tree_depth = d num_leaves = k ** d # to make things easier, we make the pessimistic assumption that # we have to store hashes for all the empty places in the tree # (when the number of blocks is not an exact exponent of k) self.subblock_overhead = 20 # the subblock hashes are organized into a k-ary tree, which # means storing (and eventually transmitting) more hashes. This # count includes all the low-level block hashes and the root. hash_nodes = (num_leaves*k - 1) / (k - 1) #print "hash_depth", d #print "num_leaves", num_leaves #print "hash_nodes", hash_nodes # the storage overhead is this self.block_storage_overhead = 20 * (hash_nodes - 1) # the transmission overhead is smaller: if we actually transmit # every subblock, we don't have to transmit 1/k of the # lowest-level subblock hashes, and we don't have to transmit the # root because it was already sent with the block-level hash tree self.block_transmission_overhead = 20 * (hash_nodes - 1 # the root - num_leaves / k) # we must get a full sibling hash chain before we can validate # any data sibling_length = d * (k-1) self.bytes_until_some_data = 20 * sibling_length + subblock_size else: raise RuntimeError("unknown mode '%s" % mode) self.storage_overhead = self.block_storage_overhead * num_blocks self.storage_overhead_percentage = 100.0 * self.storage_overhead / file_size def dump(self): for k in ("mode", "file_size", "seg_size", "num_segs", "num_subblocks", "num_blocks", "blocks_needed", "subblock_size", "block_size", "subblock_arity", "subblock_tree_depth", "subblock_overhead", "block_storage_overhead", "block_transmission_overhead", "storage_overhead", "storage_overhead_percentage", "bytes_until_some_data"): print k, getattr(self, k) def fmt(num, trim=False): if num < KiB: #s = str(num) + "#" s = "%.2f#" % num elif num < MiB: s = "%.2fk" % (num / KiB) elif num < GiB: s = "%.2fM" % (num / MiB) elif num < TiB: s = "%.2fG" % (num / GiB) elif num < PiB: s = "%.2fT" % (num / TiB) else: s = "big" if trim: s = re.sub(r'(\.0+)([kMGT#])', lambda m: m.group(2), s) else: s = re.sub(r'(\.0+)([kMGT#])', lambda m: (" "*len(m.group(1))+m.group(2)), s) if s.endswith("#"): s = s[:-1] + " " return s def text(): opts = Args() opts.parseOptions() mode = opts["mode"] arity = opts["arity"] # 0123456789012345678901234567890123456789012345678901234567890123456 print "mode=%s" % mode, " arity=%d" % arity print " storage storage" print "Size blocksize overhead overhead k d alacrity" print " (bytes) (%)" print "------- ------- -------- -------- ---- -- --------" #sizes = [2 ** i for i in range(7, 41)] radix = math.sqrt(10); expstep = 2 radix = 2; expstep = 2 #radix = 10; expstep = 1 maxexp = int(math.ceil(math.log(1e12, radix)))+2 sizes = [radix ** i for i in range(2,maxexp,expstep)] for file_size in sizes: s = Sizes(mode, file_size, arity) out = "" out += "%7s " % fmt(file_size, trim=True) out += "%7s " % fmt(s.block_size) out += "%8s" % fmt(s.storage_overhead) out += "%10.2f " % s.storage_overhead_percentage out += " %4d" % int(s.subblock_arity) out += " %2d" % int(s.subblock_tree_depth) out += " %8s" % fmt(s.bytes_until_some_data) print out def graph(): # doesn't work yet import Gnuplot opts = Args() opts.parseOptions() mode = opts["mode"] arity = opts["arity"] g = Gnuplot.Gnuplot(debug=1) g.title("overhead / alacrity tradeoffs") g.xlabel("file size") g.ylabel("stuff") sizes = [2 ** i for i in range(7, 32)] series = {"overhead": {}, "alacrity": {}} for file_size in sizes: s = Sizes(mode, file_size, arity) series["overhead"][file_size] = s.storage_overhead_percentage series["alacrity"][file_size] = s.bytes_until_some_data g.plot([ (fs, series["overhead"][fs]) for fs in sizes ]) raw_input("press return") if __name__ == '__main__': text() #graph()