Showing of Bitcoin's Proof of Work difficulty is calculated and changed.

bitcoin_block_difficulty_analysis.py

import datetime

###################################################################
#
# Showing the way bits, difficulty, target, and hash work together.
#
###################################################################

print "Calculating target from bits, verifying the block's hash is valid, and verify the calculated difficulty."

def pad_leading_zeros(hex_str):
  hex_num_chars = hex_str[2:-1]
  num_zeros_needed = 64 - len(hex_num_chars)
  padded_hex_str = '0x%s%s' % ('0' * num_zeros_needed, hex_num_chars)
  return padded_hex_str


def run_difficulty_information(bits, block_difficulty, block_hash):

  target = get_target_from_bits(bits)
  padded_hex_target = pad_leading_zeros(hex(target))

  #making sure that the block's hash is less than the target
  block_hash_hex = '0x%s' % block_hash
  block_hash_int = int(block_hash, 16)
  assert block_hash_hex < padded_hex_target
  assert block_hash_int < target
  print 'Padded target hex: %s' % padded_hex_target
  print 'Block hash in hex: %s' % block_hash_hex

  calculated_difficulty = get_difficulty_from_bits(bits)
  allowed_error = 0.01
  assert abs(float(block_difficulty) - calculated_difficulty) <= allowed_error
  print 'Difficulty: %s' % block_difficulty
  print 'Calculated Difficulty: %s' % calculated_difficulty

  print #print that new line


#genesis block
print 'Block 0'
difficulty = '1.0'
bits = '486604799'
block_hash = '000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f'
run_difficulty_information(bits, difficulty, block_hash)

#first block with difficulty not 1.0
print 'Block 32256'
difficulty = '1.18'
bits = '486594666'
block_hash = '000000004f2886a170adb7204cb0c7a824217dd24d11a74423d564c4e0904967'
run_difficulty_information(bits, difficulty, block_hash)

#block 11138
print 'Block 111388'
difficulty = '55589.52'
bits = '453062093'
block_hash = '00000000000019c6573a179d385f6b15f4b0645764c4960ee02b33a3c7117d1e'
run_difficulty_information(bits, difficulty, block_hash)

#block 493955
print 'Block 493955'
difficulty = '1364422081125.15'
bits = '402705995'
block_hash = '000000000000000000af4c179fcd65679f659947b0af164433fc1b99a186ff48'
run_difficulty_information(bits, difficulty, block_hash)




################################################################
#
# Shows how difficulty is changed when BLOCK_NUMBER % 2016 == 0
#
################################################################

print "Adjusting difficulty after every 2016 blocks"


def get_target_from_bits(bits):
  if type(bits) == str:
    bits = int(bits)
  shift = bits >> 24
  value = bits & 0x007fffff
  value <<= 8 * (shift - 3)
  return value

def get_difficulty_from_bits(bits):
  difficulty_one_target = 0x00ffff * 2 ** (8 * (0x1d - 3))
  target = get_target_from_bits(bits)
  calculated_difficulty = difficulty_one_target / float(target)
  return calculated_difficulty

def get_bits_from_target(target):
  bitlength = target.bit_length() + 1 #look on bitcoin cpp for info
  size = (bitlength + 7) / 8
  value = target >> 8 * (size - 3)
  value |= size << 24 #shift size 24 bits to the left, and taks those on the front of compact
  return value


TARGET_TIMESPAN = 1209600

def change_target(prev_bits, starting_time_secs, prev_time_secs):
  old_target = get_target_from_bits(int(prev_bits))
  time_span = prev_time_secs - starting_time_secs
  time_span_seconds = int(time_span.total_seconds())
  new_target = old_target
  new_target *= time_span_seconds
  new_target /= TARGET_TIMESPAN
  return new_target