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Computer Architecture and Operating Systems

Course taught at Faculty of Computer Science of Higher School of Economics

Final Test: Computer Architecture

The grade formula is as follows:

Grade = 0.4 * Theory + 0.6 * Programming

Part 1. Theoretical Questions

Answer the theoretical questions in a few sentences (1-2 paragraphs for a question).

Use your own words. Copy-paste from external sources and other students will result in 100% penalty.

  1. Describe how integer and floating-point values are represented in the binary format: unsigned integers, 2’s complement signed integers, and single-precision floating-point. Give an explanation with an examples of how a signed and unsigned integer values are added.

  2. Describe the concept of pipeline. List the 5 stages and give brief descriptions for them. What advantages and disadvantages does pipelining have?

  3. Give a brief definition of an interrupt. For what reasons can it be raised? Briefly explain how interrupt handler is implemented. What main actions does it perform? List the main CSR registers used for interrupt handling.

Part 2. Programming Task

Write a RISC-V assembly program that inputs integer value x and calculates the value of the f(x) function according to the specified equations. f(x) must be implemented as a function and must comply with RISC-V calling conventions.

The implemented function must use callee-saved registers (s0, s1, etc.) to store intermediate results of calculations. These registers must be saved to the stack and restored when the function returns.

Example of an f(x) function:

f(x) = 5*x + -5 if x < -9
f(x) = -5 if x >= -9
f(x) = -10*x + 10 if x == 3
f(x) = 2*x^8 - 5*x^4 + 10*x^3 - 4*x if x > 9

Variants

Choose your variant number according to your number in the list of students.

Note: the ^ symbol means “power”.

Group 191

  1. Variant 
      f(x) = -9*x + -4 if x < -10
  f(x) = -1 if x >= -10
  f(x) = 1*x^5 - 4*x^4 - 8*x^2 + 8*x if x == -2
  f(x) = 6*x + 3 if x > 2
  2. Variant 
      f(x) = 8*x + -10 if x < -4
  f(x) = 3*x + -1 if x >= -4
  f(x) = 3 if x == 0
  f(x) = 9*x^8 - 9*x^5 - 1*x^2 - 2*x if x > 4
  3. Variant 
      f(x) = 7 if x < -3
  f(x) = 3*x + -2 if x >= -3
  f(x) = 7*x^8 + 3*x^5 - 1*x^4 + 6*x if x == 4
  f(x) = 3*x + 5 if x > 8
  4. Variant 
      f(x) = -7*x + 5 if x < -10
  f(x) = -3*x + 7 if x >= -10
  f(x) = 6*x^8 + 10*x^4 + 7*x^3 - 5*x if x == -5
  f(x) = -6 if x > 4
  5. Variant 
      f(x) = 3 if x < -10
  f(x) = 6*x^7 - 3*x^6 - 5*x^3 - 7*x if x >= -10
  f(x) = -3*x + 3 if x == 1
  f(x) = -8*x + 2 if x > 6
  6. Variant 
      f(x) = 1*x^8 + 8*x^5 - 6*x^4 + 4*x if x < -1
  f(x) = 2*x + 5 if x >= -1
  f(x) = 5*x + -5 if x == 1
  f(x) = 2 if x > 2
  7. Variant 
      f(x) = 6*x^5 - 8*x^4 - 4*x^2 + 9*x if x < -2
  f(x) = -6 if x >= -2
  f(x) = -4*x + -7 if x == 2
  f(x) = 9*x + 5 if x > 6
  8. Variant 
      f(x) = 4*x^7 + 5*x^5 - 7*x^3 + 5*x if x < -6
  f(x) = 1*x + -3 if x >= -6
  f(x) = -10 if x == -3
  f(x) = 5*x + -5 if x > 0
  9. Variant 
      f(x) = 2 if x < -9
  f(x) = -7*x + -9 if x >= -9
  f(x) = 2*x^8 + 9*x^5 - 2*x^2 - 10*x if x == -4
  f(x) = -10*x + -8 if x > 0
  10. Variant 
      f(x) = 9 if x < -9
  f(x) = 8*x + -9 if x >= -9
  f(x) = 9*x^8 + 10*x^7 + 9*x^4 - 5*x if x == -6
  f(x) = -6*x + -6 if x > 9
  11. Variant 
      f(x) = -5 if x < -2
  f(x) = -7*x + -5 if x >= -2
  f(x) = -5*x + 5 if x == 2
  f(x) = 8*x^5 + 6*x^4 + 9*x^2 - 1*x if x > 9
  12. Variant 
      f(x) = 10*x^8 - 1*x^6 - 5*x^4 - 5*x if x < 0
  f(x) = 2*x + -3 if x >= 0
  f(x) = 4 if x == 5
  f(x) = 8*x + 8 if x > 7
  13. Variant 
      f(x) = 3*x^7 - 3*x^5 + 6*x^3 + 5*x if x < -1
  f(x) = -3*x + 5 if x >= -1
  f(x) = 2*x + -6 if x == 5
  f(x) = -7 if x > 9
  14. Variant 
      f(x) = 4*x^8 + 2*x^5 - 6*x^3 + 5*x if x < -6
  f(x) = -6*x + -4 if x >= -6
  f(x) = -9*x + 3 if x == -4
  f(x) = 7 if x > 7
  15. Variant 
      f(x) = 2*x + 6 if x < -6
  f(x) = 9 if x >= -6
  f(x) = 5*x^6 - 8*x^5 - 4*x^3 + 3*x if x == -5
  f(x) = 2*x + -9 if x > -4
  16. Variant 
      f(x) = 2 if x < -1
  f(x) = 10*x^8 - 1*x^6 + 4*x^3 + 7*x if x >= -1
  f(x) = 4*x + 9 if x == 4
  f(x) = -9*x + 10 if x > 6
  17. Variant 
      f(x) = 1*x + -6 if x < -9
  f(x) = -5*x + 7 if x >= -9
  f(x) = 9*x^8 + 1*x^4 - 1*x^3 - 10*x if x == -1
  f(x) = -10 if x > 7
  18. Variant 
      f(x) = 4*x + 6 if x < 7
  f(x) = -9 if x >= 7
  f(x) = -1*x + -10 if x == 8
  f(x) = 2*x^8 - 7*x^7 + 2*x^2 + 4*x if x > 9
  19. Variant 
      f(x) = -5 if x < -5
  f(x) = -2*x + -10 if x >= -5
  f(x) = -10*x + 8 if x == -2
  f(x) = 9*x^8 - 1*x^7 + 1*x^6 - 9*x if x > 8
  20. Variant 
      f(x) = 9*x^8 - 4*x^5 - 4*x^3 - 6*x if x < -6
  f(x) = -9 if x >= -6
  f(x) = -8*x + -10 if x == -4
  f(x) = 6*x + -1 if x > 8
  21. Variant 
      f(x) = 10*x^8 - 6*x^5 + 2*x^3 - 9*x if x < -8
  f(x) = -10 if x >= -8
  f(x) = -9*x + 5 if x == -1
  f(x) = -1*x + -3 if x > 9
  22. Variant 
      f(x) = 6 if x < 1
  f(x) = 10*x + -7 if x >= 1
  f(x) = 5*x^5 + 6*x^4 + 10*x^3 - 1*x if x == 2
  f(x) = 2*x + -7 if x > 9
  23. Variant 
      f(x) = 8 if x < 1
  f(x) = 6*x^8 - 7*x^6 + 2*x^5 + 6*x if x >= 1
  f(x) = -10*x + -4 if x == 4
  f(x) = -8*x + 8 if x > 6
  24. Variant 
      f(x) = 1*x + 7 if x < -8
  f(x) = -9*x + -2 if x >= -8
  f(x) = 9*x^7 + 3*x^5 - 4*x^3 - 7*x if x == 5
  f(x) = -2 if x > 9
  25. Variant 
      f(x) = 5*x + -1 if x < -6
  f(x) = 10*x^8 + 7*x^7 + 5*x^3 + 8*x if x >= -6
  f(x) = 3*x + 9 if x == 4
  f(x) = 3 if x > 8
  26. Variant 
      f(x) = -6*x + -9 if x < -10
  f(x) = -6*x + -1 if x >= -10
  f(x) = 2 if x == -1
  f(x) = 2*x^8 - 4*x^6 + 10*x^3 + 9*x if x > 5

Group 192

  1. Variant 
      f(x) = 10*x^6 - 8*x^4 + 7*x^3 + 5*x if x < -6
  f(x) = -10*x + -9 if x >= -6
  f(x) = 9*x + 9 if x == -4
  f(x) = 7 if x > 0
  2. Variant 
      f(x) = -6 if x < 1
  f(x) = 7*x^7 - 3*x^5 + 9*x^2 - 7*x if x >= 1
  f(x) = 2*x + -7 if x == 2
  f(x) = 2*x + -1 if x > 5
  3. Variant 
      f(x) = -3*x + 6 if x < -6
  f(x) = -7*x + -2 if x >= -6
  f(x) = 6*x^5 - 9*x^3 + 3*x^2 - 9*x if x == -3
  f(x) = -4 if x > 8
  4. Variant 
      f(x) = 8*x + 10 if x < -6
  f(x) = 1 if x >= -6
  f(x) = -7*x + 5 if x == 4
  f(x) = 3*x^8 - 6*x^5 + 8*x^3 - 1*x if x > 5
  5. Variant 
      f(x) = -7*x + -3 if x < -9
  f(x) = -9 if x >= -9
  f(x) = -6*x + 8 if x == -5
  f(x) = 7*x^8 - 4*x^3 - 6*x^2 - 6*x if x > 3
  6. Variant 
      f(x) = -1*x + 10 if x < -9
  f(x) = 2*x^7 + 4*x^6 + 5*x^5 + 5*x if x >= -9
  f(x) = 7*x + 1 if x == -1
  f(x) = -4 if x > 3
  7. Variant 
      f(x) = -3 if x < -5
  f(x) = 1*x + -6 if x >= -5
  f(x) = 5*x + -10 if x == -3
  f(x) = 1*x^8 - 10*x^7 + 9*x^2 + 7*x if x > 7
  8. Variant 
      f(x) = -5 if x < -6
  f(x) = 3*x + -7 if x >= -6
  f(x) = 6*x^6 + 1*x^5 + 1*x^3 + 10*x if x == 0
  f(x) = -4*x + -1 if x > 9
  9. Variant 
      f(x) = 9 if x < -6
  f(x) = 5*x^6 + 3*x^5 - 2*x^4 - 3*x if x >= -6
  f(x) = 9*x + 1 if x == 0
  f(x) = 2*x + -10 if x > 5
  10. Variant 
      f(x) = 8*x^8 + 7*x^5 + 9*x^3 + 10*x if x < -10
  f(x) = 8*x + -9 if x >= -10
  f(x) = -6*x + -4 if x == -3
  f(x) = -5 if x > 1
  11. Variant 
      f(x) = 5*x^7 + 3*x^5 + 5*x^4 + 10*x if x < -10
  f(x) = 5*x + 6 if x >= -10
  f(x) = 9*x + 5 if x == 6
  f(x) = 8 if x > 7
  12. Variant 
      f(x) = -3 if x < 4
  f(x) = 4*x + -3 if x >= 4
  f(x) = 7*x + -6 if x == 6
  f(x) = 2*x^6 - 4*x^3 - 8*x^2 - 10*x if x > 7
  13. Variant 
      f(x) = 4*x + -10 if x < -9
  f(x) = 10*x^5 - 2*x^4 - 2*x^2 + 7*x if x >= -9
  f(x) = -7 if x == -2
  f(x) = -9*x + 4 if x > -1
  14. Variant 
      f(x) = 4*x + 6 if x < 1
  f(x) = -4 if x >= 1
  f(x) = 3*x^5 - 6*x^3 - 5*x^2 + 10*x if x == 8
  f(x) = 4*x + 8 if x > 9
  15. Variant 
      f(x) = 5*x^8 + 4*x^4 - 4*x^2 + 3*x if x < -1
  f(x) = -9*x + -3 if x >= -1
  f(x) = -9 if x == 0
  f(x) = 8*x + -9 if x > 2
  16. Variant 
      f(x) = 6*x^7 - 7*x^5 - 6*x^4 - 10*x if x < -4
  f(x) = -7*x + -3 if x >= -4
  f(x) = 2*x + 8 if x == -3
  f(x) = -1 if x > 4
  17. Variant 
      f(x) = 7*x + 10 if x < -5
  f(x) = -9 if x >= -5
  f(x) = 5*x + -9 if x == -2
  f(x) = 6*x^5 + 4*x^3 + 9*x^2 + 10*x if x > 7
  18. Variant 
      f(x) = -3*x + 7 if x < -2
  f(x) = -10*x + 10 if x >= -2
  f(x) = 8*x^8 - 6*x^5 + 3*x^3 + 5*x if x == 3
  f(x) = -2 if x > 8
  19. Variant 
      f(x) = 1*x^8 + 9*x^6 - 6*x^4 + 5*x if x < -4
  f(x) = 9 if x >= -4
  f(x) = 8*x + -8 if x == 6
  f(x) = 2*x + 6 if x > 7
  20. Variant 
      f(x) = -6*x + 3 if x < -10
  f(x) = 7*x + 8 if x >= -10
  f(x) = 8 if x == -1
  f(x) = 10*x^8 + 1*x^3 + 9*x^2 - 6*x if x > 9
  21. Variant 
      f(x) = -1 if x < -8
  f(x) = -2*x + -7 if x >= -8
  f(x) = 4*x^6 - 6*x^4 + 2*x^2 - 7*x if x == 1
  f(x) = -2*x + 5 if x > 8
  22. Variant 
      f(x) = 8*x + 8 if x < -10
  f(x) = 8 if x >= -10
  f(x) = 6*x^5 - 8*x^4 + 9*x^3 - 3*x if x == 4
  f(x) = 8*x + 2 if x > 9
  23. Variant 
      f(x) = 2*x^6 - 2*x^5 + 2*x^4 - 1*x if x < 1
  f(x) = -9*x + 4 if x >= 1
  f(x) = -9 if x == 6
  f(x) = -4*x + 3 if x > 8
  24. Variant 
      f(x) = -9 if x < 7
  f(x) = -4*x + -2 if x >= 7
  f(x) = -1*x + -5 if x == 8
  f(x) = 7*x^6 - 8*x^5 - 6*x^4 + 9*x if x > 9
  25. Variant 
      f(x) = 6*x + -10 if x < -7
  f(x) = 6*x^6 - 4*x^4 + 7*x^2 + 5*x if x >= -7
  f(x) = 6 if x == -2
  f(x) = -1*x + 5 if x > 6
  26. Variant 
      f(x) = 10 if x < -2
  f(x) = -3*x + 10 if x >= -2
  f(x) = -10*x + -5 if x == 1
  f(x) = 4*x^7 - 5*x^4 + 4*x^2 + 8*x if x > 2
  27. Variant 
      f(x) = 2 if x < -5
  f(x) = 2*x^7 + 2*x^6 + 8*x^5 - 2*x if x >= -5
  f(x) = -1*x + 4 if x == 5
  f(x) = 2*x + -9 if x > 7

Group 193

  1. Variant 
      f(x) = -8*x + -6 if x < -10
  f(x) = -3*x + -7 if x >= -10
  f(x) = 10 if x == -9
  f(x) = 2*x^7 + 9*x^6 - 10*x^5 - 1*x if x > 2
  2. Variant 
      f(x) = 2*x^7 - 3*x^4 + 6*x^3 - 5*x if x < -6
  f(x) = 4 if x >= -6
  f(x) = -5*x + 2 if x == 0
  f(x) = -7*x + -10 if x > 5
  3. Variant 
      f(x) = -6 if x < -9
  f(x) = -5*x + 6 if x >= -9
  f(x) = 9*x^8 - 2*x^3 - 4*x^2 - 4*x if x == -5
  f(x) = 6*x + 7 if x > 1
  4. Variant 
      f(x) = 1 if x < -4
  f(x) = 8*x + 5 if x >= -4
  f(x) = 10*x + -3 if x == -1
  f(x) = 4*x^7 + 5*x^4 + 8*x^3 - 4*x if x > 1
  5. Variant 
      f(x) = -1*x + 6 if x < -9
  f(x) = -10 if x >= -9
  f(x) = 8*x^8 - 2*x^7 + 5*x^5 + 3*x if x == -2
  f(x) = -9*x + 6 if x > 4
  6. Variant 
      f(x) = -3*x + 7 if x < -8
  f(x) = 2*x + -7 if x >= -8
  f(x) = 1 if x == -5
  f(x) = 5*x^7 + 10*x^4 - 2*x^2 - 4*x if x > 4
  7. Variant 
      f(x) = -3 if x < -10
  f(x) = -8*x + -5 if x >= -10
  f(x) = -6*x + -6 if x == -7
  f(x) = 7*x^7 - 10*x^5 - 2*x^2 - 4*x if x > 4
  8. Variant 
      f(x) = 3*x + 1 if x < 5
  f(x) = -2*x + -4 if x >= 5
  f(x) = 5*x^7 + 9*x^4 - 7*x^3 - 3*x if x == 6
  f(x) = -4 if x > 7
  9. Variant 
      f(x) = 4*x^7 - 2*x^3 + 7*x^2 + 10*x if x < -1
  f(x) = 1 if x >= -1
  f(x) = 2*x + -3 if x == 5
  f(x) = -4*x + -7 if x > 7
  10. Variant 
      f(x) = 9*x^6 + 9*x^4 + 8*x^2 + 9*x if x < -6
  f(x) = -6 if x >= -6
  f(x) = 2*x + 10 if x == -4
  f(x) = -4*x + -10 if x > 9
  11. Variant 
      f(x) = -8*x + 10 if x < -8
  f(x) = 2*x + 6 if x >= -8
  f(x) = 2 if x == 4
  f(x) = 9*x^5 + 5*x^4 + 7*x^3 - 5*x if x > 7
  12. Variant 
      f(x) = -9*x + -2 if x < -5
  f(x) = -6 if x >= -5
  f(x) = 9*x^8 + 4*x^5 + 9*x^4 - 1*x if x == -4
  f(x) = 7*x + -2 if x > 5
  13. Variant 
      f(x) = 3*x + -6 if x < 0
  f(x) = 9*x^7 - 1*x^4 - 3*x^3 - 5*x if x >= 0
  f(x) = -7 if x == 8
  f(x) = 5*x + 6 if x > 9
  14. Variant 
      f(x) = -4 if x < -8
  f(x) = -7*x + 8 if x >= -8
  f(x) = 6*x + 7 if x == -2
  f(x) = 2*x^8 - 7*x^5 + 5*x^2 - 8*x if x > 7
  15. Variant 
      f(x) = 2*x^8 - 3*x^3 - 5*x^2 + 9*x if x < 1
  f(x) = -1*x + 6 if x >= 1
  f(x) = -9 if x == 3
  f(x) = -10*x + -8 if x > 6
  16. Variant 
      f(x) = -9*x + 2 if x < -8
  f(x) = 7 if x >= -8
  f(x) = 5*x^8 + 1*x^6 - 1*x^3 - 5*x if x == 5
  f(x) = -8*x + 10 if x > 9
  17. Variant 
      f(x) = 4*x + 8 if x < 1
  f(x) = 3*x^7 + 6*x^4 + 3*x^3 - 3*x if x >= 1
  f(x) = 7*x + 1 if x == 3
  f(x) = -9 if x > 6
  18. Variant 
      f(x) = 6*x^8 + 1*x^7 - 6*x^3 + 8*x if x < -9
  f(x) = -9*x + 8 if x >= -9
  f(x) = -7 if x == 3
  f(x) = -7*x + 4 if x > 5
  19. Variant 
      f(x) = -5*x + 5 if x < -2
  f(x) = -8 if x >= -2
  f(x) = 3*x^7 + 8*x^6 - 5*x^5 - 9*x if x == -1
  f(x) = -3*x + -7 if x > 5
  20. Variant 
      f(x) = -3*x + 8 if x < -1
  f(x) = 2*x^7 - 8*x^6 - 2*x^2 - 3*x if x >= -1
  f(x) = -6*x + 4 if x == 3
  f(x) = 10 if x > 6
  21. Variant 
      f(x) = 3*x + -7 if x < -3
  f(x) = 4*x + -3 if x >= -3
  f(x) = 10*x^5 - 8*x^4 + 6*x^2 - 8*x if x == -1
  f(x) = -10 if x > 3
  22. Variant 
      f(x) = 5*x + 9 if x < -6
  f(x) = -4*x + -4 if x >= -6
  f(x) = 2*x^8 + 4*x^4 - 5*x^2 - 4*x if x == -1
  f(x) = 7 if x > 0
  23. Variant 
      f(x) = -3 if x < -10
  f(x) = 7*x + 9 if x >= -10
  f(x) = 7*x^8 - 1*x^4 - 4*x^3 - 1*x if x == -1
  f(x) = -1*x + -7 if x > 9
  24. Variant 
      f(x) = 9*x + 3 if x < -9
  f(x) = 8 if x >= -9
  f(x) = 7*x^5 - 3*x^3 - 4*x^2 - 4*x if x == 4
  f(x) = -3*x + -7 if x > 9
  25. Variant 
      f(x) = -4 if x < -6
  f(x) = -6*x + 10 if x >= -6
  f(x) = 1*x^8 + 10*x^6 - 5*x^4 - 1*x if x == 1
  f(x) = 2*x + 6 if x > 4
  26. Variant 
      f(x) = -2*x + -7 if x < -4
  f(x) = 1 if x >= -4
  f(x) = -8*x + 8 if x == 0
  f(x) = 6*x^7 - 9*x^5 - 7*x^3 - 2*x if x > 4
  27. Variant 
      f(x) = 5*x^7 + 10*x^6 + 10*x^5 + 6*x if x < -2
  f(x) = -3*x + -1 if x >= -2
  f(x) = -7 if x == 2
  f(x) = 4*x + 7 if x > 4