text: # Go deh!
  
  Mainly Tech projects on Python and Electronic Design Automation.
  
  # Egyptian division
  
  Egyptian division is a method of dividing integers using addition and doubling that is similar to the algorithm of Ethiopian multiplicaion
  
  ## Algorithm:
  
  Given two numbers where the dividend is to be divided by the divisor:
  1. Start the construction of a table of two columns: `powers_of_2`, and `doublings`; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
  2. Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
  3. Continue with successive i'th rows of 2^i and 2^i * divisor.
  4. Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
  5. We now assemble two separate sums that both start as zero, called here answer and accumulator
  6. Consider each row of the table, in the reverse order of its construction.
  7. If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
  8. When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
  (And the remainder is given by the absolute value of accumulator - dividend).
  
  ## Example: 580 / 34
  
  ### Table creation:
  
  powers_of_2doublings
  134
  268
  4136
  8272
  16544
  
  134
  268
  4136
  8272
  16544
  00
  
  ### Considering table rows, bottom-up:
  
  When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
  134
  268
  4136
  8272
  1654416544
  134
  268
  4136
  827216544
  16544
  134
  268
  413616544
  8272
  16544
  134
  26816544
  4136
  8272
  16544
  13417578
  268
  4136
  8272
  16544
  
  ### Finally
  
  So 580 divided by 34 using the Egyptian method is `17` remainder (578 - 580) or `2`.
  
  # Rosetta Code
  
  This blog post should be a Rosetta Code task, but at the time of writing the site has been down for maintenance for a week. I will still writethe task description and its first Python solution though.
  
  The task is to create a function that does Egyptian division. The function should closely follow the description above in using a list/array of powers of two, and another of doublings.
  • Functions should be clear interpretations of the algorithm.
  • Use the function to divide 580 by 34 and show the answer here, on this page.
  
  # Python Solution
  
  In [2]:
  ```def egyptian_divmod(dividend, divisor):
  assert divisor != 0
  pwrs, dbls = [1], [divisor]
  while dbls[-1] <= dividend:
  pwrs.append(pwrs[-1] * 2)
  dbls.append(pwrs[-1] * divisor)
  ans, accum = 0, 0
  for pwr, dbl in zip(pwrs[-2::-1], dbls[-2::-1]):
  if accum + dbl <= dividend:
  accum += dbl
  ans += pwr
  return ans, abs(accum - dividend)
  
  # Test it gives the same results as the divmod built-in
  from itertools import product
  for i, j in product(range(13), range(1, 13)):
  assert egyptian_divmod(i, j) == divmod(i, j)
  
  # Mandated result
  i, j = 580, 34
  print(f'{i} divided by {j} using the Egyption method is %i remainder %i'
  % egyptian_divmod(i, j))
  ```
  ```580 divided by 34 using the Egyption method is 17 remainder 2
  ```
  
  # Extra
  
  A quick note on hardware applications.
  The astute may note that the doublings column entries are easily computed as successive shifts of the binary representation of the divisor; and that the result in binary can be read off by marking 1 if a table row is summed or 0 if it is not.
explanation: The document provides a detailed explanation of the Egyptian division method, including an algorithm, an example, and a Python implementation. It also includes a test to verify the correctness of the implementation and an application of the method to divide 580 by 34, yielding the result 17 with a remainder of 2. The document does not contain a question but rather a detailed explanation and an example of the method.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Go deh!
  
  Mainly Tech projects on Python and Electronic Design Automation.
  
  # Egyptian division
  
  Egyptian division is a method of dividing integers using addition and doubling that is similar to the algorithm of Ethiopian multiplicaion
  
  ## Algorithm:
  
  Given two numbers where the dividend is to be divided by the divisor:
  1. Start the construction of a table of two columns: `powers_of_2`, and `doublings`; by a first row of a 1 (i.e. 2^0) in the first column and 1 times the divisor in the first row second column.
  2. Create the second row with columns of 2 (i.e 2^1), and 2 * divisor in order.
  3. Continue with successive i'th rows of 2^i and 2^i * divisor.
  4. Stop adding rows, and keep only those rows, where 2^i * divisor is less than or equal to the dividend.
  5. We now assemble two separate sums that both start as zero, called here answer and accumulator
  6. Consider each row of the table, in the reverse order of its construction.
  7. If the current value of the accumulator added to the doublings cell would be less than or equal to the dividend then add it to the accumulator, as well as adding the powers_of_2 cell value to the answer.
  8. When the first row has been considered as above, then the integer division of dividend by divisor is given by answer.
  (And the remainder is given by the absolute value of accumulator - dividend).
  
  ## Example: 580 / 34
  
  ### Table creation:
  
  powers_of_2doublings
  134
  268
  4136
  8272
  16544
  
  134
  268
  4136
  8272
  16544
  00
  
  ### Considering table rows, bottom-up:
  
  When a row is considered it is shown crossed out if it is not accumulated, or bold if the row causes summations.
  134
  268
  4136
  8272
  1654416544
  134
  268
  4136
  827216544
  16544
  134
  268
  413616544
  8272
  16544
  134
  26816544
  4136
  8272
  16544
  13417578
  268
  4136
  8272
  16544
  
  ### Finally
  
  So 580 divided by 34 using the Egyptian method is `17` remainder (578 - 580) or `2`.
  
  # Rosetta Code
  
  This blog post should be a Rosetta Code task, but at the time of writing the site has been down for maintenance for a week. I will still writethe task description and its first Python solution though.
  
  The task is to create a function that does Egyptian division. The function should closely follow the description above in using a list/array of powers of two, and another of doublings.
  • Functions should be clear interpretations of the algorithm.
  • Use the function to divide 580 by 34 and show the answer here, on this page.
  
  # Python Solution
  
  In [2]:
  ```def egyptian_divmod(dividend, divisor):
  assert divisor != 0
  pwrs, dbls = [1], [divisor]
  while dbls[-1] <= dividend:
  pwrs.append(pwrs[-1] * 2)
  dbls.append(pwrs[-1] * divisor)
  ans, accum = 0, 0
  for pwr, dbl in zip(pwrs[-2::-1], dbls[-2::-1]):
  if accum + dbl <= dividend:
  accum += dbl
  ans += pwr
  return ans, abs(accum - dividend)
  
  # Test it gives the same results as the divmod built-in
  from itertools import product
  for i, j in product(range(13), range(1, 13)):
  assert egyptian_divmod(i, j) == divmod(i, j)
  
  # Mandated result
  i, j = 580, 34
  print(f'{i} divided by {j} using the Egyption method is %i remainder %i'
  % egyptian_divmod(i, j))
  ```
  ```580 divided by 34 using the Egyption method is 17 remainder 2
  ```
  
  # Extra
  
  A quick note on hardware applications.
  The astute may note that the doublings column entries are easily computed as successive shifts of the binary representation of the divisor; and that the result in binary can be read off by marking 1 if a table row is summed or 0 if it is not.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of the Egyptian division method, including an algorithm, an example, and a Python implementation. It also includes a test to verify the correctness of the implementation and an application of the method to divide 580 by 34, yielding the result 17 with a remainder of 2. The document does not contain a question but rather a detailed explanation and an example of the method.
  
  Label: no-question