The Joys of Being Wrong, the diligence of DUer "SunSeeker", and the Elimination of the Penny

[Bernardo de La Paz]

1. Python program

from math import floor
from random import random
import sys

version = "v0.3"
print (f'TransactRound {version}')
print (f'python {sys.version [0: 7]}n')

prices = []
price_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # 10 tails
coi = [0, 0, 0, 0, 0]
diffs_count = [0, 0, 0, 0, 0]
total_diffs = 0
sim_num = 0
numbers_of_items = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5]



def price_range (tail, count) :
for _ in range (count):
price = rand_price (tail)
prices.append (price)
price_counts [tail] += 1



def rand_price (tail:int) -> float:
while True:
price = floor (random () * 99) * 10 + tail
if price >= 20:
return price



def print_results (num:int) :
print (f'nCount {num: 9, } :',
f'1 item: {100*(coi[0]/num):4.1f}%, ',
f'2: {100*(coi[1]/num):4.1f}%, ',
f'3: {100*(coi[2]/num):4.1f}%, ',
f'4: {100*(coi[3]/num):4.1f}%, ',
f'5: {100*(coi[4]/num):4.1f}%.')
print (f'Diffs counts: -2:{(diffs_count [0]/num)*100:5.1f} %, ',
f'-1:{(diffs_count [1]/num)*100:5.1f} %, ',
f'0:{(diffs_count [2]/num)*100:5.1f} %, ',
f'1:{(diffs_count [3]/num)*100:5.1f} %, ',
f'2:{(diffs_count [4]/num)*100:5.1f} %.')
print (f'Total_diffs {total_diffs:,}:',
f' per transaction: {total_diffs / num:5.3f} cents.')



def simulate (count:int, title:str, tax_percent:float=0.0, pr_sample:bool=False ):
'''
tax_rate 0.0 is silent.
tax_rate < 0.0 means use random tax rates
'''
global coi, diffs_count
coi = [0, 0, 0, 0, 0]
diffs_count = [0, 0, 0, 0, 0]

if tax_percent == 0.0:
taxing:bool = False
else:
taxing:bool = True
if tax_percent < 0.0:
tax_rate_random = True
else:
tax_rate = tax_percent / 100
tax_rate_random = False

global sim_num
sim_num += 1

title = f'Simulation {sim_num}: {title}'
if taxing:
if tax_rate_random:
title += ' with random tax rates'
else:
title += f' with tax rate {tax_percent} %'
print (f'nn{title}n')

if pr_sample or ((sim_num % 4) == 1):
out = f'Percent last digit:n'
for i in range (10):
out += f'{i}: {price_counts /40:4.1f} %n'
print (out)

diff_round = [0, -1, -2, 2, 1]
if pr_sample:
print ('First 20 transactions:n')
item_str = ''

global total_diffs
total_diffs = 0
for i in range (count):
num_items = numbers_of_items [int (random () * 20)]
coi [num_items - 1] += 1
total = 0
for j in range (num_items):
index = floor (random () * 3998.9)
item = prices [index]
if i < 20:
item_str += f' {item/100:5.2f}'
total += item

if taxing:
if tax_rate_random:
tax_rate = 0.0025 * int (46 * random ())
tax = round (total * tax_rate)
total_w_tax = total + tax
tax_str = f' tax rate {tax_rate*100:4.1f}%,'
tax_str += f' tax {tax/100:5.2f}, total w tax {total_w_tax/100:5.2f},'

else:
total_w_tax = total
tax_str = ""

digit = total_w_tax % 5
diff = diff_round [digit]
diffs_count [2 + diff] += 1
cash = total_w_tax + diff
total_diffs += diff
if pr_sample and (i < 20):
out = f'items {num_items}: '
out += f' total {total/100:5.2f},'
out += tax_str
out += f' diff {diff:2},'
out += f' cash {cash/100:5.2f}:'
out += f' {item_str}'
print (f'{(i+1):2}: {out}')
item_str = ''
condition = False
else:
condition = (i == count / 1000) or (i == count / 100) or
(i == count / 10)
if condition:
print_results (i)

print_results (count)
print (f'nEnd of {title}.')



count = 20 * 1000 * 1000
count = 200 * 1000

prices = []
price_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # 10 tails

price_range (0, 400)
price_range (5, 3600)

print ('Simulation of Rounding on large numbers of Transactions')
print (' by a method like Lombra, Easter Economic Journal, v27n4, Fall 2001n')

print (f'Size of prices {len (prices)}')

simulate (count, "Prices rounded to 0 or 5 cents" )
simulate (count, "Prices rounded to 0 or 5 cents", 5.0)
simulate (count, "Prices rounded to 0 or 5 cents", 11.25)
simulate (count, "Prices rounded to 0 or 5 cents", -99)

prices = []
price_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # 10 tails

price_range (0, 400); price_range (1, 400); price_range (2, 400);
price_range (3, 400); price_range (4, 400); price_range (5, 400);
price_range (6, 400); price_range (7, 400); price_range (8, 400);
price_range (9, 400)

simulate (count, "Prices random tails" )
simulate (count, "Prices random tails", 5.0)
simulate (count, "Prices random tails", 11.25)
simulate (count, "Prices random tails", -99)

prices = []
price_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # 10 tails

# 4 * percent * 10. Lombra data.
price_range (0, 4 * 2); price_range (1, 4 * 1); price_range (2, 4 * 2)
price_range (3, 4 * 5); price_range (4, 4 * 90); price_range (5, 4 * 37)
price_range (6, 4 * 29); price_range (7, 4 * 1); price_range (8, 4 * 8)
price_range (9, 4 * 825)

simulate (count, "Lombra distribution of prices", 0.0, True)
simulate (count, "Lombra distribution of prices", 5.0)
simulate (count, "Lombra distribution of prices", 11.25, True)
simulate (count, "Lombra distribution of prices", -99)

prices = []
price_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # 10 tails

price_range (9, 4 * 800)
price_range (8, 4 * 80)
price_range (5, 4 * 60)
price_range (4, 4 * 20)
price_range (7, 4 * 20)
price_range (0, 4 * 16)
price_range (1, 4 * 1)
price_range (2, 4 * 1)
price_range (3, 4 * 1)
price_range (6, 4 * 1)

simulate (count, "Imagined distribution of prices", 0.0, True)
simulate (count, "Imagined distribution of prices", 5.0)
simulate (count, "Imagined distribution of prices", 11.25)
simulate (count, "Imagined distribution of prices", -99)

print ('nFini.')